01 - Preheat the oven to 350°F. Grease and line an 8-inch round cake pan with parchment paper.
02 - In a large bowl, whisk together flour, granulated sugar, baking powder, salt, cinnamon, and nutmeg.
03 - Rub the cold, cubed butter into the dry ingredients using your fingertips until the mixture resembles coarse crumbs.
04 - Add the sliced apples to the flour mixture and toss to coat evenly.
05 - In a separate bowl, whisk eggs, milk, and vanilla extract together until blended.
06 - Pour the wet mixture over the apple mixture and gently fold until just combined.
07 - Transfer the batter to the prepared cake pan, spreading evenly. Sprinkle turbinado or demerara sugar over the top for a crunchy crust.
08 - Bake for 45–50 minutes, or until a skewer inserted into the center comes out clean and the top is golden. Let cool in the pan for 15 minutes, then transfer to a wire rack.
09 - While the cake bakes, heat the milk in a medium saucepan over medium heat until just steaming, not boiling.
10 - Whisk egg yolks, sugar, and cornstarch in a bowl until smooth.
11 - Gradually whisk the hot milk into the egg mixture, then return to the saucepan. Cook over low heat, stirring constantly, until thickened and coating the back of a spoon, about 5–7 minutes. Do not boil. Remove from heat and stir in vanilla extract.
12 - Serve slices of warm apple cake with a generous pour of custard.